A) \[\frac{3}{7}\]
B) \[\frac{8}{25}\]
C) \[\frac{7}{25}\]
D) \[\frac{13}{25}\]
Correct Answer: B
Solution :
| [b]\[\sin \theta -\cos \theta =\frac{3}{5}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,{{(\sin \theta -\cos \theta )}^{2}}=\frac{9}{25}\] |
| \[\Rightarrow \,\,\,\,\,{{\sin }^{2}}\theta +{{\cos }^{2}}\theta -2\sin \theta \cdot \cos \theta =\frac{9}{25}\] \[[{{\sin }^{2}}\theta +{{\cos }^{2}}\theta =1]\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,1-2\sin \theta \cdot \cos \theta =\frac{9}{25}\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,2\sin \theta \cdot \cos \theta =\frac{16}{25}\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\sin \theta \cdot \cos \theta =\frac{8}{25}\] |
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